During the Yugoslav wars, Nesterović moved to PAOK of the Greek League. While playing there, he obtained a second citizenship (Greek) to avoid EU restrictions. To obtain Greek citizenship he had to administratively change his name in the eyes of Greek law. While in Greece and other EU countries, he thus competed as a domestic player under the name Radoslav "Rasho" Makris.[4][5]

Ahead of the 1995–96 season, Nesterović returned to his hometown to play for Union Olimpija. Competing in the Slovenian domestic league, his averages were 30 minutes, 17 points and 14 rebounds per game. The summer of 1996 off season brought another significant feat for Nesterović; while playing for Slovenia's youth national team he was named the MVP at the 1996 FIBA Europe Under-20 Championship. The next season, 1996–97, he was part of that legendary Olimpija team that reached the 1997 EuroLeague Final Four in Rome. In that season, he played an average of 17.0 minutes per game, averaging 8.0 points, and 4.3 rebounds per game in the EuroLeague.[6]

The exposure on the biggest European stage led to a big time move for Nesterović to the Italian League power Virtus (Kinder) Bologna during the summer of 1997. In the first season with his new club, he scored an average of 8 points and grabbed an average of 6 rebounds per game,[7] in the Italian domestic league. In the EuroLeague, he scored 6.5 points and grabbed 6.0 rebounds per game.[8] He helped Virtus win the EuroLeague title, playing alongside legendary players such as Sašha Danilović, Zoran Savić, and Antoine Rigaudeau. In the EuroLeague Final, Nesterović scored 6 points and grabbed 9 rebounds.[9]

Nesterović stayed in Minnesota for four full seasons because he played only the last two regular-season games, plus all of his team's games in the playoffs, in his first season. His best season with the Timberwolves was 2002–03, when he averaged 11.2 points and 6.6 rebounds per game, earning himself a 6-year contract with the San Antonio Spurs in 2004. Although the Timberwolves were offering him a contract worth $12 million more, Nesterović opted for the move to Texas for a shot at the NBA title.[10]

In his first season with San Antonio, Nesterović scored 8.7 points per game and grabbed 7.7 rebounds per game. In his second season with the Spurs, 2004–05, he suffered an ankle injury, and was limited to 70 games. Nevertheless, he remained the starting center for the majority of the season, and, along with his colleague from the Slovenian national basketball team, Beno Udrih, he ultimately won an NBA title with the Spurs that year.

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